Entanglement of midspectrum eigenstates of chaotic many-body systems: Reasons for deviation from random ensembles

Abstract

Eigenstates of local many-body interacting systems that are far from spectral edges are thought to be ergodic and close to being random states. This is consistent with the eigenstate thermalization hypothesis and volume-law scaling of entanglement. We point out that systematic departures from complete randomness are generically present in mid-spectrum eigenstates, and focus on the departure of the entanglement entropy from the random-state prediction. We show that the departure is (partly) due to spatial correlations and due to orthogonality to the eigenstates at the spectral edge, which imposes structure on the mid-spectrum eigenstates.

arXiv comment8 pages, 5 figures, 122 references + 6 pages, 9 figures in 8 Appendices

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